For fxx37x28x16 Find f10using synthetic division Is 10 a zer

For f(x)=x^3-7x^2+8x+16, Find f(10)using synthetic division. Is 10 a zero of the function?Explain in a complete sentence. Use synthetic division to determine if x+1 is a factor of f(x). Is -1 a zero of the function?Explain in a complete sentence. List all of the zeros of the polynomial Write the polynomial function as a product of linear factors.

Solution

given

f(x) = x^3 -7x^2 +8x +16

finding f(10)

1 -7 8 16

10 10 30 380

-----------------------------------------------

1 3 38 396

so f(10) = 396

b). NO . \'10\' is not a zero function

if it is a zero function then f(10) wolud be zero

c). to check x+1 is factor of f(x)

x+1=0

x=-1

-1 1 -7 8 16

-1 8 -16

--------------------------------------------------------------

1 -8 16 0

so x+1 is factor of f(x)

d). yes it is a zero function since f(-1) =0

e) . f(x) = (x+1) (x^2 - 8x +16)

f(x) = (x+1) (x-4)^2

so zero polynominals are -1, 4,4

f)

f(x) = (x+1) (x-4)^2

f(x) = (x+1) (x-4) (x-4)